Finite Group Databasebeta

C2×#20245029 #26368999

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245029

Splittings

SylowC47 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#13093939
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
Fitting, prime radicalC2×C47×#525C2
socleC22×C47C2×#99
cosocleC2×D4×C47C24
hypercenterC2×#525D47
hypocenterC47C2×#2120
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#525

1398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322289);